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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.06042 |
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| _version_ | 1866908638909562880 |
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| author | Song, Fanghui Wang, Zhongjian Sun, Jiebao |
| author_facet | Song, Fanghui Wang, Zhongjian Sun, Jiebao |
| contents | We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (HJ) residual in the OT formulation with the original flow matching loss function. Our approach avoids inner optimization subproblems that are present in previous one-step OFM approaches. During the prediction stage, our approach supports both one-step (Brenier-map) and multi-step ODE sampling from the same learned potential, leveraging the straightness of the OT flow. We validate scalability and performance on standard OT benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching Song, Fanghui Wang, Zhongjian Sun, Jiebao Machine Learning We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (HJ) residual in the OT formulation with the original flow matching loss function. Our approach avoids inner optimization subproblems that are present in previous one-step OFM approaches. During the prediction stage, our approach supports both one-step (Brenier-map) and multi-step ODE sampling from the same learned potential, leveraging the straightness of the OT flow. We validate scalability and performance on standard OT benchmarks. |
| title | Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.06042 |